As a first benchmark, we consider for an ideal gas the two dimensional inviscid isentropic vortex also studied in [1]}, [2]}. For this test, an analytic solution is available, that can be used to assess the convergence properties of the scheme. The initial conditions are given as a perturbation of a reference state
\(\rho (\mathbf {x},0) = \rho _\infty + \delta \rho \qquad \mathbf {u}(\mathbf {x},0) = \mathbf {u}_{\infty } + \delta \mathbf {u} \qquad p(\mathbf {x},0) = p_{\infty } + \delta p\) 
